You may have to pay damages if it can be shown that you were negligent in letting your dog run loose.
the car that that did the original striking will pay for all damages.
The state of NY is not going to pay for damages to your car if you hit a deer. You need to make a police report and contact your car insurance agent.
The owner of the car that caused your damages will be responsible to pay damages to you unless you live in a no-fault state. In that case, your insurance pays for your damages.
95% of the time, if a person hits you from the back its their fault. So their insurance company will have to pay for their damages to your vehicle and body.
Than you have to pay for the damages of your car.
The other person pays.
Only if the insured car was at fault.
I am assuming that you are making up some abbreviation by using the plpd. The part of the policy that would pay for the damages to the car you hit if it was your fault would be Property Damage Liability Coverage.
If you have full coverage on your car, then your insurance should pay. But if all you have is liability insurance, then no, it won't pay to fix your car. But there is a chance that your uninsured motorists coverage will pay for the damages, if you have it.
If you know who hit your car, and they have insurance, then, yes, they should pay for it, so long as you were not parked illegally. Let YOUR insurance company handle this for you. That's what you pay them for.